I did something similar with an animated 3d character. I overlayed “frost” in AE & the character wiped a circle in the screen to look through. It looked pretty good.
I used a combination of adjustment layers & textures.
From memory…
Adjustment layer added blur, a slight blue-ish tint and desaturation & some displacement from the ice layer above to simulate looking through a sheet of ice.
I had a couple of different photos of ice & ice cracks at varying layers of opacity above. I played around with different ways of getting transparency such as mapping luminance to the alpha channel.. basically until it looked right.
I then just made an animated luma matte to “wipe” away the adjustment and texture layers as appropriate. (In your case the animated text)
Hope that helps a bit.